PROBLEM1:SIMPLELINEARREGRESSION“BY HAND”(80POINTSPOSSIBLE)The following chart shows observations…

PROBLEM1:SIMPLELINEARREGRESSION“BY HAND”(80POINTSPOSSIBLE)The following chart shows observations for six combinations ofPRICE (X)andSALES (Y)oflemonadeon a given day acrossmultiple sellers.(transactions)PriceSalesIXY1.308521.00403.50754.75505.506062.0080A)Enter theSALESandPRICEdata into Excel. What “type” of data is this? Explain what other types ofdata may be used to examine this relationship.B)The general equation for a linear relationship isSALES=??+??*PRICE.Suppose that an initial (non-OLS) estimation gives coefficients of?????????????????????In Excel,show a scatter plot of observations and the linear relationship given the suggested values of???????Provide an interpretation of the intercept and slopecoefficients given here.What do the valuesmean?C)You now have an estimate of the economic relationship. Calculate the “explained” portion ofSALESand the unexplained, or residual, part ofSALES.The fitted,explained, or deterministicportion ofSALESfor each observationiis:??????^= b0+ b1xPRICEiThe residualor unexplained portion ofSALESfor each observationiis:??^= SALESi-SALESHAT,i2?Provide a table of “fitted” and“residual”values forSALESiover the6observations.?Whichobservation has the largest residual?D)You now want to determine how well the economic theory explains the observedrelationship betweenSALESandPRICE. You also want to determine how good your “best-fit” line is relative to other options.?Calculateyoursum of the residual valuesover the 6observations. What isdesirable for this sum? What does your sum of residuals tell you about your line??Calculateyoursum of thesquaredresidual valuesover the 6observations. Whatis desirable for this sum? What does your sum of residuals tell you about your line?E)The simple-minded alternative to the economic theory is to simply calculate the mean forSALESover the sample and use that as our fitted dependent variable.?Calculate the mean forSALESover the 6observations. Does the mean provide asgoodanexplanation for the behavior ofSALESas your line?Why or why not? Bespecific (what is the sum of squared residuals)?F)In the context of this example, explainwhy there exists an error or residual term and exactlywhat it represents.G)Finally, calculate theordinary least squares estimatesfor???and??. Do not use the Excelregression function (that’s cheating), rather calculate the components “by hand” and plugthem into the OLS formula. Show your work.H)Show that the OLS estimates are “better” than the values given in part (B) above. Explainyour answer.I)Enter the data intoStatato check your answers above. ShowStataoutput of the regression“REGRESSYX”(where Y = dependent, X = independent)

 

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